Essentially this is a very slow shutter speed of about 1/25 of a second which enables the subject to become 'blurred'. Compare this to a shutter of about 1/4000 for the normal surfing shots on here and you will understand the differences in speed. Because of the slow shutter, in order to maintain correct exposure, the aperture is as small as the lens permits and ISO as low as your camera will go (when in bright daylight like this).
The trick then is to pan (vertically and hortizontally) and predict the movement of the surfer to have a part of the photo remain still whilst the majority of the frame shows movement blur. All it takes is for an arm, the board, even a shadow to remain sharp for this effect to work.
You will see this technique used in motor racing to show speed. The other side effect is an almost 3D appearance especially when you see water moving through the air in a variety of directions.